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Search: id:A039993
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| A039993 |
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Number of different primes embedded in n. |
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+0
8
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| 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 3, 1, 1, 1, 3, 0, 1, 1, 1, 1, 3, 1, 2, 1, 2, 1, 2, 1, 3, 3, 1, 2, 3, 1, 4, 2, 1, 0, 1, 1, 2, 0, 1, 0, 2, 0, 0, 1, 1, 2, 3, 1, 1, 1, 2, 1, 2, 0, 1, 1, 1, 0, 1, 0, 2, 0, 0, 1, 3, 2, 4, 2, 2, 2, 1, 1, 3, 0, 0, 1, 2, 0, 1, 0, 1, 0, 1, 0, 1, 2, 1, 0, 2, 0, 3, 1, 0, 0, 2, 1, 4, 2, 1
(list; graph; listen)
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OFFSET
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1,13
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COMMENT
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a(n) counts permuted subsequences of digits of n which denote primes.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
C. K. Caldwell, The Prime Glossary, Primeval Number
J. P. Delahaye, Primes Hunters, 1379 is very primeval (in French)
M. Keith, Integers Containing Many Embedded Primes
W. Schneider, Primeval Numbers
G. Villemin's Almanach of Numbers, Mike Keith's Primeval Number
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EXAMPLE
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a(17) = 3 since we can obtain 7, 17 and 71. a(22) = 1, since we can get only one prime (in contrast, A075053(22) = 2).
a(1013) = 14 because the prime subsets derived from the digital permutations of 1013 are {3, 11, 13, 31, 101, 103, 113, 131, 311, 1013, 1031, 1103, 1301, 3011}.
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MATHEMATICA
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Needs["DiscreteMath`Combinatorica`"]; f[n_] := Block[{a = Drop[ Sort[ Subsets[ IntegerDigits[n]]], 1], b = c = {}, k = 1, l}, l = Length[a] + 1; While[k < l, b = Append[b, Permutations[ a[[k]] ]]; k++ ]; b = Union[ Flatten[b, 1]]; l = Length[b] + 1; k = 1; While[k < l, c = Append[c, FromDigits[ b[[k]] ]]; k++ ]; Count[ PrimeQ[ Union[c]], True]]; Table[ f[n], {n, 1, 105}]
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CROSSREFS
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Different from A075053. For records see A072857, A076497. See also A134596, A134597.
Cf. A039999.
Adjacent sequences: A039990 A039991 A039992 this_sequence A039994 A039995 A039996
Sequence in context: A138361 A030408 A068153 this_sequence A075053 A007362 A060268
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KEYWORD
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nonn,base
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AUTHOR
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David W. Wilson (davidwwilson(AT)comcast.net)
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EXTENSIONS
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Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 25 2002
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